Question

14. (i) Examine whether 7 + 3x is a factor of 3x3 + 7x.
INCERT]
(ii) Examine whether x + 2 is a factor of the polynomials x3 + 3x2 + 5x + 6 and 2x + 4.
INCERT]
NICORTI​

Answer 1

Answer:

i) (7 + 3x) is not a factor of (3x³ + 7x).

ii) (x + 2) is a factor of both (x³ + 3x² + 5x + 6) & (2x + 4).

Step-by-step explanation:

i) F(x) = 3x³ + 7x

f(x) = 7 + 3x

if F(x) = 0 for f(x) = 0 then f(x) will be a factor of F(x)

f(x) = 0

=> 7 + 3x = 0

=> x = -7/3

F(-3/7) = 3(-7/3)³ + 7(-7/3)

= -1029/27 - 49/3

= -1470/27

≠ 0

therefore (7 + 3x) is not a factor of (3x³ + 7x).

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ii) F(x) = x³ + 3x² + 5x + 6

P(x) = 2x + 4

f(x) = x + 2

if F(x) = 0 and P(x) = 0 for f(x) = 0 then f(x) will be a factor of F(x) and P(x)

f(x) = 0

=> x + 2 = 0

=> x = -2

F(-2) = (-2)³ + 3(-2)² + 5(-2) + 6

= -8 + 12 - 10 + 6

= 0

therefore (x + 2) is a factor of (x³ + 3x² + 5x + 6).

P(-2) = 2(-2) + 4

= -4 + 4

= 0

therefore (x + 2) is a factor of (2x + 4).